World number one Dinara Safina fought back to beat unseeded 19-year-old German Sabine Lisicki and reach the semi-finals at Wimbledon.

The Russian won 6-7 (5-7) 6-4 6-1 in soaring temperatures on Centre Court.

She will next face defending champion Venus Williams, who thrashed Agnieszka Radwanska 6-1 6-2 despite some heavy strapping on her knee.

Serena Williams overpowered Victoria Azarenka and will face Elena Dementieva in the other semi-final on Friday.

Dementieva, the fourth seed, power through with a 6-2 6-2 thrashing of Italian Francesca Schiavone.

Safina went into the first quarter-final on Centre Court as the favourite against Lisicki, but the Russian had never previously been past the third round and has been no great fan of grass in the past.

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Mental toughness was key - Safina

Lisicki, on other hand, was far deeper into uncharted territory having only once before made the third round at a Grand Slam.

However, the German was on a high after beating ninth seed Caroline Wozniacki in the previous round and she broke serve first in the quarter-final when Safina double-faulted in game three.

Lisicki was serving beautifully as she moved 5-3 clear, saving a couple of break points in game four, but the nerves took hold and she was pegged back to a tie-break.

Again it was the German who took the initiative but she looked in trouble when two set points went begging, until Safina handed over a woeful double-fault on the third.

The frustrated Russian was warned for racquet abuse early in the second set but she regained her composure to break for 4-3 and served out, saving a break-back point in the process.

A tense final set looked to be on the cards but Safina dominated, breaking twice in a row and holding her nerve during a lengthy medical time-out as Lisicki received treatment on her calf.

The 23-year-old broke once again for a victory that keeps her on track to end he Grand Slam drought, but she will need to improve drastically on the 15 double faults she gave up.

"I think I was Santa Claus serving so many double faults," said Safina. "On the practice court I don't serve a single one.

"The serve is there, I just have to put the brain there. I know what I have to do, I'm just not doing it.

"I was hanging in there. I was tough mentally, I think that was the key."

Lisicki said: "I just went out there to fight. I gave it all I had, but she was physically fitter than me."

Venus Williams wasted little time in seeing off the 11th seed Radwanska.

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Venus dreaming of all-Williams final

The American, 29, had too much power and athleticism as she won in 68 minutes on Court One.

The champion clambered all over the Radwanska serve from the start and, despite some valiant scrambling from the Pole, Williams converted her fourth break point to go 2-0 clear.

Within 18 minutes the American was 5-0 up and when Radwanska, 20, did get on the board it only provided temporary relief, and the chance for the crowd to finally get involved, before Williams wrapped up the set in 28 minutes with an ace.

Radwanska looked to be coping better with the pace at the start of the second but it still came as a shock when she got to 0-40 in game two and converted her first chance to break.

It was hardly a crisis for Williams, however, and she broke twice in succession before firing a magnificent cross-court backhand winner to get to 5-2, and sealed victory soon after with a huge forehand into the corner.

"She plays the ball so low and so fast, I'm happy to get through," Williams told BBC Sport.

Do I feel invincible? I'd like to say yes, but I really do work at it

Venus Williams

"I'm in the semi-finals of Wimbledon, it's where I want to be and I'm looking to go further."

Asked about a possible final against her sister, she added: "That would be fantastic, it's what Serena and I want, but we still have to play well and bring our best tennis to the the court."

The sisters, the only two Grand Slam winners left in the women's field, have dominated Wimbledon in recent years, with Venus winning five singles titles and Serena two.

"Do I feel invincible? I'd like to say yes, but I really do work at it. To close these matches out takes a lot of work," said Venus.

"We are definitely the front-runners in tennis as far as being some of the best players out there.

"I just think that the style of game that Serena and I play, that particular style, we play better than the other women."

Radwanska admitted that in hot, fast conditions, it was almost impossible to defeat Venus.

"She was serving and hitting the ball so strongly. Her game is so powerful, it was very hard to do anything on the court," she said.

"It's so hard to break her when she's serving at 120mph. Venus and Serena are so different to other opponents."

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